# Unified Uncertainties: Combining Input, Data and Model Uncertainty into a Single Formulation

arXiv: https://arxiv.org/abs/2406.18787 · HTML: https://mlsanity.com/paper/2406.18787/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 26 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [DropConnect Is Effective in Modeling Uncertainty of Bayesian Deep Networks](https://mlsanity.com/paper/1906.04569/) (2019)
- [A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement](https://mlsanity.com/paper/2204.09308/) (2022)
- [Linear Maximum Margin Classifier for Learning from Uncertain Data](https://mlsanity.com/paper/1504.03892/) (2015)
- [The information of attribute uncertainties: what convolutional neural networks can learn about errors in input data](https://mlsanity.com/paper/2108.04742/) (2021)

## Built on by (most cited first, 3 of 3)

- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [DeepUQ: Assessing the Aleatoric Uncertainties from two Deep Learning Methods](https://mlsanity.com/paper/2411.08587/) (2024)
- [An Analysis of Temporal Dropout in Earth Observation Time Series for Regression Tasks](https://mlsanity.com/paper/2504.06915/) (2025)

## Abstract (arXiv)

Modelling uncertainty in Machine Learning models is essential for achieving safe and reliable predictions. Most research on uncertainty focuses on output uncertainty (predictions), but minimal attention is paid to uncertainty at inputs. We propose a method for propagating uncertainty in the inputs through a Neural Network that is simultaneously able to estimate input, data, and model uncertainty. Our results show that this propagation of input uncertainty results in a more stable decision boundary even under large amounts of input noise than comparatively simple Monte Carlo sampling. Additionally, we discuss and demonstrate that input uncertainty, when propagated through the model, results in model uncertainty at the outputs. The explicit incorporation of input uncertainty may be beneficial in situations where the amount of input uncertainty is known, though good datasets for this are still needed.